Topology Identification of Directed Graphs via Joint Diagonalization of Correlation Matrices

Discovering connectivity patterns of directed networks is a crucial step to understand complex systems such as brain-, social-, and financial networks. Several existing network topology inference approaches rely on structural equation models (SEMs). These presume that exogenous inputs are available, which may be unrealistic in certain applications. Recently, an alternative line of work reformulated SEM-based topology identification as a three-way tensor decomposition task. This way, knowing the exogenous input correlation statistics (rather than the exogenous inputs themselves) suffices for network topology identification. The downside is that this approach is computationally expensive. In addition, it is hard to incorporate prior information of the network structure (e.g., sparsity and local smoothness) into this framework, while such prior information may help enhance performance when handling real-world noisy data. The present work puts forth a joint diagonalizaition (JD)-based approach to directed network topology inference. JD can be viewed as a variant of tensor decomposition, but features more efficient algorithms, and can readily account for the network structure. Different from existing alternatives, novel identifiability guarantees are derived regardless of the exogenous inputs or their statistics. Three JD algorithms tailored for network topology inference are developed, and their performance is showcased using simulated and real data tests.